Signal processing system employing time and frequency domain partitioning

ABSTRACT

The present invention relates to a method for processing a digital input signal by a Finite Impulse Response, FIR, filtering means, comprising partitioning the digital input signal at least partly in the time domain to obtain at least two partitions of the digital input signal; partitioning the FIR filtering means in the time domain to obtain at least two partitions of the FIR filtering means; Fourier transforming each of the at least two partitions of the digital input signal to obtain Fourier transformed signal partitions; Fourier transforming each of the at least two partitions of the FIR filtering means to obtain Fourier transformed filter partitions; performing a convolution of the Fourier transformed signal partitions and the corresponding Fourier transformed filter partitions to obtain spectral partitions; combining the spectral partitions to obtain a total spectrum; and inverse Fourier transforming the total spectrum to obtain a digital output signal.

BACKGROUND OF THE INVENTION

1. Priority Claim

This application claims the benefit of priority from EP 06014253, filedJul. 10, 2006, and to EP 07011621, filed Jun. 13, 2007, both of whichare incorporated herein by reference.

2. Technical Field

The present disclosure relates to a signal processing system and, moreparticularly, to a signal processing system that employs time andfrequency domain partitioning.

3. Related Art

Signal processing systems are used in a wide range of applications. Oneset of applications includes speech signal processing/recognition, wherethe signal processing system may be used to enhance the intelligibilityof the speech signals. Another such application is the enhancement ofthe quality of signals transmitted and/or received in a communicationsystem. Wired and/or wireless communication between two parties may becarried out where one or both of the parties are present in a noisybackground environment. One example of such a communication environmentis a hands-free voice communication and/or command system in a vehicle.Signal processing in such communication systems may be used to reducebackground noise and to enhance the intelligibility of the speechsignals.

Other problems also exist in such communication environments. Forexample, the signals of one party may be emitted by a loudspeaker in thereceiving party's environment. These omissions may be picked up by themicrophone used by the remote party. If picked-up by the microphone,transmissions from the remote party may include unpleasant echoes thatmay affect the quality and intelligibility of the voice conversation. Incertain circumstances, acoustic feedback may lead to a completebreakdown of communication.

To overcome such echo/feedback problems, the communication system mayinclude a signal processing system that is configured as an echocanceller. In an echo canceller, a replica of the acoustic feedbackresponse may be synthesized and a compensation signal may be obtainedfrom the received signal at the loudspeaker. This compensation signalmay be subtracted from the signal of the microphone to generate thesignal that is transmitted from the remote party.

Communication systems, speech processing/recognition systems, and othersystems may also use one or more equalization filters to enhance thequality of the subject speech signal as well as the transmitted and/orreceived signals. The equalization filters operate on the acousticsignals by boosting or attenuating the signals over a pre-determinedfrequency range. The equalization filter may include one or moreshelving filters for selectively boosting/attenuating either the low orhigh frequency range. The equalization filter may also include one ormore peaking filters for boosting/attenuating signals with the centerfrequency, bandwidth in-band and out-of-band gains being separatelyadjustable. Still further, the equalization filter may be in the form ofa parametric equalizer that combines one or more shelving filters andpeaking filters.

The filters used in such signal processing systems may include digitalfilters that are implemented in hardware and/or software. Digitalfilters may include Finite Impulse Response (FIR) filters and InfiniteImpulse Response (IIR) filters. Each of these digital filter types hasadvantages and disadvantages that make them suitable for specificapplications. FIR filters are very stable but may require the use of asignificant number of filter coefficients. These filter coefficientsused by the digital filter may be adapted or optimized to enhance thequality of the processed audio signal. The large number of coefficients,adaptation, and optimization may impose very large memory requirementsand a heavy processor load on the signal processing system therebymaking the use of FIR filters impractical in some systems. IIR filtersmay be easier to implement, particularly for equalization filters usedin audio applications having high sampling rates (e.g., 44.1 KHz). FIRfilters at such high sampling rates may have the aforementionedproblems. However, IIR filters may have stability issues because thefilter topology employs feedback.

Other filter types include short filters designed in a distortedfrequency range, so-called warped FIR or IIR filters. Warped filters,however, also suffer from the need for a long computation time. In analternative approach, multirate digital systems or filter banks fordividing the audio signal that is to be processed into multiplefrequency ranges by parallel band pass filters have been used forequalizing. However, this approach may suffer from high memoryrequirements and a high latency. Accordingly, there is a need for asignal processing system employing an improved digital filter topology.

SUMMARY

A signal processing system operates on an input signal using time andfrequency domain partitioning. A converter is used to convert thedigital input signal to provide a first plurality of Fourier transformedsignal partitions. A filter signal source is used to provide a pluralityof Fourier transformed filter partitions. The partitions of theconverter and the filter signal source are provided to a convolutionprocessor that uses the partitions to generate a plurality of convolutedpartitioned output signals. The convoluted partitioned output signalsmay be combined to generate a total spectrum signal that may be inverseFourier transformed to provide a processed digital output signal.

Other systems, methods, features and advantages of the invention willbe, or will become, apparent to one with skill in the art uponexamination of the following figures and detailed description. It isintended that all such additional systems, methods, features andadvantages be included within this description, be within the scope ofthe invention, and be protected by the following claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention can be better understood with reference to the followingdrawings and description. The components in the figures are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention. Moreover, in the figures, likereferenced numerals designate corresponding parts throughout thedifferent views.

FIG. 1 is a signal processing system that employs time and frequencydomain partitioning.

FIG. 2 is a second signal processing system that employs time andfrequency domain partitioning.

FIG. 3 is a third signal processing system that employs time andfrequency domain partitioning.

FIG. 4 is a fourth signal processing system that employs time andfrequency domain partitioning.

FIG. 5 is a diagram of a hands-free voice communications system that mayemploy a signal processing system.

FIG. 6 is a diagram of a speech processing system that may employ asignal processing system.

FIG. 7 is a diagram of one platform on which a signal processing systemmay be implemented.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1 is a diagram of a signal processing system 100 that employs timeand frequency domain partitioning. The signal processing system 100receives a digital input signal x[n] for processing at the input of afirst time partitioner 105. The digital input signal x[n] may correspondto a speech signal that has been subject to an analog-to-digitalconversion process. The first time partitioner 105 is adapted topartition the digital input signal x[n] in the time domain into aplurality of time domain partitioned input signals x_(i)[n], where i isan integer index. The time domain partitioned input signals x_(i)[n] aresubject to a Fourier transform operation by a Fourier transformprocessor, such as Fast Fourier Transform (FFT) processor 110. Theresulting Fourier transform signals are provided as a plurality ofFourier transform signal partitions X_(i)(ω) that correspond to the timedomain partitioned input signals X_(i)[n].

The processing system 100 also includes an FIR filter 115 having afilter response FIR(n). The output FIR(n) of the FIR filter 115 isprovided to the input of a second time partitioner 120. The second timepartitioner is adapted to partition the FIR filter in the time domaininto a plurality of time domain partitioned FIR signals FIR_(i)[n]. Thesignal processing system 100 may use the same number of FIR partitionsFIR_(i)[n] as input signal partitions x_(i)[n]. The plurality of timedomain partitioned Fourier signals FIR_(i)[n] are subject to a Fouriertransform operation by a Fourier transform processor, such as FFTprocessor 125. In practice, the FFT may be carried out using theCooley-Tukey algorithm, although other FFT algorithms may also beemployed. The latency of the transformation process may be determined bythe length of the chosen FFT and, for example, may be given by twice theFFT length N_(F). In order to carry out fast convolutions, the filterpartitions FIR_(i)[n] may be Fast Fourier transformed to obtain theFourier transformed filter partitions FIR_(i)(ω) in the followingmanner:

${{{FIR}_{i}(\omega)} = {\sum\limits_{n = 0}^{N_{F} - 1}{{x\lbrack n\rbrack}{\exp \left( {{- \frac{2{\pi }}{N_{F}}}n\; \omega} \right)}}}},$

The resulting Fourier transform signals are provided as a plurality ofFourier transformed filter partitions FIR_(i)(ω) that correspond to thetime domain partitioned Fourier signals FIR_(i)[n]. While the pluralityof Fourier transformed filter partitions may be generated duringoperation of the signal processing system 100, the Fouriertransformations may be executed off-line and stored in system memory 127in certain instances where, for example, the response of the FIR filter115 is fixed.

The plurality of Fourier transformed filter partitions FIR_(i)(ω) andthe plurality of Fourier transform signal partitions X_(i)(ω) areconvoluted with one another by a convolution processor 130. In thoseinstances in which the Fourier transform signal partitions arecalculated off-line, the values corresponding to the plurality ofFourier transform filter partitions FIR_(i)(ω) may be retrieved from thesystem memory 127 by the convolution processor 130 for processing. Theoutput of the convolution processor 130 is in the form of a plurality ofconvoluted partitioned output signals Y_(i)(ω). The plurality ofconvoluted partitioned output signals Y_(i)(ω) may be provided to theinput of a combiner/adder 135 that combines the plurality of convolutedpartitioned output signals to generate a total spectrum output signalY(ω). The total spectrum output signal Y(ω) is provided to the input ofan Inverse Fast Fourier Transform processor 140 to transform the totalspectrum output signal Y(ω) to a digital output signal y[n]. The digitaloutput signal y[n] corresponds to a filtered/processed version of thedigital input signal x[n]. In symbolic notation, the output signal y[n]corresponds to the following equation:

${y\lbrack n\rbrack} = {{{{IFFT}\left( {Y(\omega)} \right)}\mspace{14mu} {with}\mspace{14mu} {Y(\omega)}} = {{\sum\limits_{i}{Y_{i}(\omega)}} = {\sum\limits_{i}{{X_{i}(\omega)} \cdot {{FIR}_{i}(\omega)}}}}}$

The digital input signal x[n] may be divided into blocks in the timedomain by the time partitioner 105, and the convolution executed by theconvolution processor 130 may be performed using an overlap-save blockconvolution. The blocks may be of equal size for straightforwardprocessing or, alternatively, have different sizes. Shorter blocks mayprovide a relatively low latency while longer blocks may make theoverall convolution operations less expensive in terms of processingpower.

The overlap-save block convolution involves the use of a long digitalinput signal that is broken into successive blocks of N_(x) samples,each block overlapping the previous block by N_(FIR) samples. Circularconvolution of each block is performed. The first N_(FIR)−1 values ineach output block are discarded, and the remaining values areconcatenated to create the output signal. A 50% overlap may be used.

Alternatively, overlap-add convolution may be used. Uniform block sizesoffer possibilities for performance optimization if the overlap-addscheme is used in the frequency domain. Overlap-add convolution may beused when the impulse response of the FIR filter 115 is shorter than theblock length N_(x).

The total spectrum signal Y(ω) may be obtained by using only half of thenumber of the Fourier components of the Fourier transformed filterpartitions FIR_(i)(ω). Efficient processing is, thus, enabled.

In the signal processing system 100, the Fourier transformed signalpartitions X_(i)(ω) and the Fourier transformed filter partitionsFIR_(i)(ω) are all of the same bandwidth and the mid frequencies aredistributed equidistant from one another in the frequency domain. Morecomplicated algorithms for the calculation of the distribution of themid frequencies are possible and might be applied depending on theactual application.

FIG. 2 is a diagram of another signal processing system 200 that employstime and frequency partitioning. In FIG. 2, the digital input signalx[n] is provided to the input of a concatenator 205. The concatenator205 sequentially concatenates the input signal x[n] for processing andoverlaps old and new digital input information as shown at data block210. The concatenated data blocks generated by concatenator 205 areprovided to the input of an FFT processor 215, which generatescorresponding Fourier transformed signal partitions X₁(ω) throughX_(p)(ω). The individual the Fourier transformed signal partitions X₁(ω)through X_(p)(ω) correspond to the spectral representation of therespective signal partitions in the time domain and can therefore bedelayed in the frequency domain to provide a complete spectralrepresentation of the input signal. Accordingly, each of the Fouriertransformed signal partitions X₁(ω) through X_(p)(ω) is delayed by anappropriate amount by delay lines 220 before being applied to the inputof a respective convolutor 225. At the respective convolutor 225, eachof the Fourier transformed signal partitions X₁(ω) through X_(p)(ω) isconvoluted with a respective one of the Fourier transformed FIRpartitions FIR₁(ω) through FIR_(p)(ω). Although the Fourier transformedFIR partitions FIR₁(ω) through FIR_(p)(ω) of FIG. 2 are provided at theoutput of FFT processor 230, the partitioned filter data FIR₁(ω) throughFIR_(p)(ω) may be provided from system memory in certain circumstances.

The convolution operations executed by the convolutors 225 result in thegeneration of a plurality of convoluted partitioned output signals Y₁(ω)through Y_(p)(ω). The plurality of convoluted partitioned output signalsY₁(ω) through Y_(p)(ω) are provided to the input of a combiner/adder 235to generate a total spectrum signal Y(ω). The total spectrum signal Y(ω)is provided to the input of an IFFT processor 240, which provides ablock output 245 that includes the data y for the digital output signaly[n]. As shown in the exemplary data block 250, the lower portion of theblock output 245 includes the data y for the digital output signal y[n]while the upper portion of the block output may be ignored/discarded.

FIG. 3 is a diagram of another signal processing system 300 that employstime and frequency partitioning. In FIG. 3, the digital input signalx[n] is provided to the input of a concatenator 305. The concatenator305 sequentially concatenates the input signal x[n] for processing andoverlaps old and new digital input information as shown at data block310. The concatenated data blocks generated by concatenator 305 aredelayed by an appropriate amount using delay lines 315 before eachdelayed signal is provided to the input of a corresponding FFT processor320. The FFT processors 320 generate a plurality of Fourier transformedsignal partitions X₁(ω) through X_(p)(ω) corresponding to the timedomain partition input signals provided at the output of the delay lines315. The Fourier transformed signal partitions X₁(ω) through X_(p)(ω)are provided to the input of respective convolutors 325 where they areeach convoluted with a respective one of the Fourier transformed FIRpartitions FIR₁(ω) through FIR_(p)(ω). Although the Fourier transformedFIR partitions FIR₁(ω) through FIR_(p)(ω) of FIG. 3 are provided at theoutput of FFT processor 330, the partition data FIR₁(ω) throughFIR_(p)(ω) may likewise be provided from system memory in certaincircumstances.

The convolution operations executed by the convolutors 325 result in thegeneration of a plurality of convoluted partitioned output signals Y₁(ω)through Y_(p)(ω). The plurality of convoluted partitioned output signalsY₁(ω) through Y_(p)(ω) are provided to the input of a combiner/adder 335to generate a total spectrum signal Y(ω). The total spectrum signal Y(ω)is provided to the input of an IFFT processor 340, which provides ablock output 345 that includes the data y for the digital output signaly[n]. As shown in the exemplary data block 350 the lower portion of theblock output 345 includes the data y for the digital output signal y[n]while the upper portion of the block output may be ignored/discarded.

FIG. 4 is a diagram of another signal processing system 400 that employstime and frequency partitioning. In FIG. 4, the digital input signalx[n] is provided to the input of a concatenator 405. The concatenator405 sequentially concatenates the input signal x[n] for processing andoverlaps old and new digital input information as shown at data block410. The concatenated data blocks generated by concatenator 405 aredelayed by an appropriate amount using delay lines 415 before eachdelayed signal is provided to the input of a corresponding FFT processor420. The FFT processors 420 generate a plurality of Fourier transformedsignal partitions X₁(ω) through X_(T)(ω) corresponding to the timedomain partition input signals provided at the output of the delay lines415. The Fourier transformed signal partitions X₁(ω) through X_(T)(ω)are provided to the input of respective convolutors 425 where they areeach convoluted with a respective one of the Fourier transformed FIRpartitions FIR₁(ω) through FIR_(T)(ω). Although the Fourier transformedFIR partitions FIR₁(ω) through FIR_(T)(ω) of FIG. 4 are provided at theoutput of FFT processor 430, the partition data FIR₁(ω) throughFIR_(T)(ω) may likewise be provided from system memory in certaincircumstances.

The convolution operations executed by the convolutors 425 result in thegeneration of a plurality of convoluted partitioned output signals Y₁(ω)through Y_(T)(ω). The plurality of convoluted partitioned output signalsY₁(ω) through Y_(T)(ω) are provided to the input of a combiner/adder435.

As shown in FIG. 4, the output of the Tth FFT processor 420 generatesthe Fourier transformed input signal X_(T)(ω) and is provided to theinput of a plurality of sequentially arranged delay lines 435. Each ofthe delay lines 435 provides its output to a corresponding concatenator440 that concatenates the delayed output signal with its respectiveFourier transformed filter partition. The output of the concatenators440 Y_(T+1)(ω) through Y_(T+S)(ω) are provided to the input of acombiner/adder 445. The output of the combiner/adder 445, in turn, iscombined with the other convoluted partitioned output signals Y₁(ω)through Y_(T)(ω) at combiner/adder 447 to generate a total spectrumsignal Y(ω). The total spectrum signal Y(ω) is provided to the input ofan IFFT processor 450, which provides a block output 455 that includesthe data y for the digital output signal y[n]. As shown in the exemplarydata block 460 the lower portion of the block output 455 includes thedata y for the digital output signal y[n] while the upper portion of theblock output may be ignored/discarded.

In FIG. 4 a combined partitioning of the digital input signal x[n] inthe time and in the spectral domain is illustrated. Different from theexample shown in FIG. 3, only part of the digital input signal x[n] ispartitioned in the time domain by means of time delay filtering. On theone hand, T partitions x₁[n], . . . , x_(T)[n] of the input signal x[n]are each Fast Fourier transformed to obtain T Fourier transformed signalpartitions X₁(ω), . . . X_(T)(ω). On the other hand, S Fouriertransformed parts of the input signal are partitioned in the spectraldomain to obtain S partitions in the spectral domain X_(T+1)(ω), . . .X_(T+S)(ω). The Fourier transformed signal partitions X₁(ω), . . . ,X_(T+S)(ω) are then convoluted with the corresponding Fouriertransformed filter partition FIR₁(ω), . . . , FIR_(T+S)(ω), and theresults Y₁(ω), . . . , Y_(T+S)(ω) are summed up to obtain the totalspectrum Y(ω).

FIG. 5 is a diagram of a hands-free voice communication system 500. InFIG. 5, a microphone 505 is connected to corresponding audio circuitry510 to facilitate voice communication with a remote party. A receiver515 provides audible communications from the remote party through aloudspeaker 520. An echo canceller 525 is used to inhibit undesiredechoes and/or feedback that may otherwise be transmitted throughtransmitter 530 to the remote party. The echo canceller 525 receivessignals from the receiver 515 and/or audio circuitry 510 for processingthrough, for example, signal processor 535. Signal processor 535 may beconfigured in the manner shown in FIGS. 1 through 4. The output of theecho canceller 525 is subtracted from the output signal of the audiocircuitry 510 at a summing circuit 540 to generate a signal fortransmission that is provided to the input of transmitter 530.

FIG. 6 is a diagram of a speech processing system 600. The speechprocessing system may include a microphone 605 that may be used by auser to provide a speech signal to corresponding audio circuitry 610.The output of the audio circuitry 610 is provided to the input of asignal processor 615. Signal processor 615 may be configured in themanner shown in FIGS. 1 through 4. The output of the signal processor615 may be provided to the input of a speech recognition engine 620that, in turn, is used to drive a target application 630. The targetapplication may be a speech-to-text application, a voice commandapplication, or other speech controlled application.

The systems shown in FIGS. 1 through 4 may be implemented in software,hardware, or a combination of software and hardware. One example of theplatform on which the signal processing systems may be implemented isshown in FIG. 7. In FIG. 7, a CPU 705 is in communication with a digitalsignal processing core 710 memory storage 715 and I/O circuitry 720.Memory storage 715 may include operating system code 725 and signalprocessing code 730 providing the signal processing instructions used toconfigure the manner in which the signal processing system is tooperate. Memory storage 715 may also include partitioned FIR data 735comprising Fourier transformed filter partition data that has beencalculated off-line. Further, memory storage 715 may be arranged toinclude networked memory, random access memory, and other memory typesto meet system demands.

In FIG. 7, a continuous time domain signal x(t) is provided to the inputof an analog-to-digital converter 740 to generate the discrete digitalinput signals x[n] for processing. Similarly, the processed digitaloutput signals y[n] are provided to the input of a digital-two-analogconverter 745 to generate a continuous output signal y(t) in the timedomain.

While various embodiments of the invention have been described, it willbe apparent to those of ordinary skill in the art that many moreembodiments and implementations are possible within the scope of theinvention. Accordingly, the invention is not to be restricted except inlight of the attached claims and their equivalents.

1. A signal processing system comprising: a converter adapted to converta digital input signal to provide a first plurality of Fouriertransformed signal partitions; a filter signal source adapted to providea plurality of Fourier transformed filter partitions; and a convolutionprocessor adapted to provide a plurality of convoluted partitionedoutput signals corresponding to a convolution of the partitions providedby the converter and the filter signal source.
 2. The signal processingsystem of claim 1, where the converter comprises: a time partitioneradapted to partition the digital input signal in the time domain into aplurality of time domain partitioned input signals; and a Fouriertransform processor adapted to provide the plurality of Fouriertransformed signal partitions corresponding to the time domainpartitioned input signal of the time partitioner.
 3. The signalprocessing system of claim 1, where the converter comprises: a Fouriertransform processor adapted to receive blocks of the digital inputsignal and to generate a Fourier transformed signal output correspondingto each block; and a plurality of delay lines connected to receive theFourier transformed signal output provided by the Fourier transformprocessor for each block, where the plurality of Fourier transformedsignal partitions correspond to output signals provided by the pluralityof delay lines.
 4. The signal processing system of claim 1, where theconverter comprises: a plurality of delay lines adapted to receiveblocks of the digital input signal to generate time delayed input signalblocks; and a plurality of Fourier transform processors respectivelyassociated with each of the plurality of delay lines to generate theplurality of Fourier transformed signal partitions.
 5. The signalprocessing system of claim 1, where the filter signal source comprises:a time partitioner adapted to partition an FIR filter in the time domaininto a plurality of time domain partitioned filter signals; and aFourier transform processor adapted to provide the plurality of Fouriertransformed filter partitions corresponding to the time domainpartitioned filter signals of the time partitioner.
 6. The signalprocessing system of claim 1, where the filter signal source comprisesoff line process Fourier transformed filter partition data stored insystem memory.
 7. A signal processing system comprising: a first timepartitioner adapted to partition a digital input signal in the timedomain into a plurality of time domain partitioned input signals; afirst Fourier transform processor adapted to provide a plurality ofFourier transformed signal partitions corresponding to the time domainpartitioned input signal provided by the first time partitioner; asecond time partitioner adapted to partition a finite impulse response(FIR) filter in the time domain into a plurality of time domainpartitioned FIR signals; a second Fourier transform processor adapted toprovide a plurality of Fourier transformed filter partitionscorresponding to the plurality of time domain partitioned FIR signals;and a convolution processor adapted to provide a plurality of convolutedpartitioned output signals corresponding to a convolution of thepartitions provided by the first and second Fourier transformprocessors.
 8. The signal processing system of claim 7, and furthercomprising a combiner adapted to combine the plurality of convolutedpartitioned output signals to obtain an output signal corresponding to atotal spectrum output signal.
 9. The signal processing system of claim8, and further comprising an inverse Fourier transform processor adaptedto perform an inverse Fourier transform operation on the total spectrumoutput signal to obtain a digital output signal.
 10. The signalprocessing system of claim 7, where the first time partitioner dividesthe input signal into blocks in the time domain, and where theconvolution processor executes an overlap-save block convolution of thepartitions provided by the first and second Fourier transformprocessors.
 11. The signal processing system of claim 7, where theplurality of Fourier transformed signal partitions of the first Fouriertransform processor and the plurality of Fourier transformed filterpartitions of the second Fourier transform processor have the samebandwidth.
 12. The signal processing system of claim 11, where theplurality of Fourier transformed signal partitions of the first Fouriertransform processor and the plurality of Fourier transformed filterpartitions of the second Fourier transform processor have frequencyresponses in which the mid frequencies are equally distributed withrespect to one another in the frequency domain.
 13. The signalprocessing system of claim 7, where the first time partitioner isadapted to partition a first portion of the input signal x[n] to obtainT partitions x_(T)[n] and a second portion of the input signal x[n] toobtain S partitions x_(S)[n], where S and T are both integers; the firstFourier transform processor is adapted to transform the input signalpartitions x_(T)[n] to obtain T Fourier transformed signal partitionsX_(T)(ω) and to transform the input signal partitions x_(S)[n] to obtainS Fourier transformed signal partitions X_(S)(ω); the second timepartitioner is adapted to provide T time domain partitioned FIR signalsFIR_(T)[n] corresponding to a first portion of the FIR filter and S timedomain partitioned FIR signals FIR_(S)[n] corresponding to a secondportion of the FIR filter; and the second Fourier transform processor isadapted to transform the T time domain partitioned FIR signalsFIR_(T)[n] to obtain corresponding Fourier transformed filter partitionsFIR_(T)(ω) and to transform the S time domain partitioned FIR signalsFIR_(T)[n] to obtain corresponding Fourier transformed filter partitionsFIR_(S)(ω).
 14. The signal processing system of claim 13, where theconvolution processor executes a convolution process on the Fouriertransformed signal partitions (X_(T)(ω) and X_(S)(ω)) and thecorresponding Fourier transformed filter partitions (FIR_(T)(ω) andFIR_(S)(ω)) to provide a plurality of convoluted partitioned outputsignals Y₁(ω), . . . , Y_(T+S)(ω).
 15. The signal processing system ofclaim 14, and further comprising a combiner adapted to combine theplurality of convoluted partitioned output signals Y₁(ω), . . . ,Y_(T+S)(ω) to obtain an output signal corresponding to a total spectrumoutput signal.
 16. A signal processing system comprising: a first timepartitioning means for partitioning a digital input signal in the timedomain into a plurality of time domain partitioned input signals; afirst Fourier transform means for transforming the plurality of timepartitioned input signals into a plurality of Fourier transformed signalpartitions; a second time partitioning means for partitioning a finiteimpulse response (FIR) filter in the time domain into a plurality oftime domain partitioned FIR signals; a second Fourier transform meansfor transforming the plurality of time domain partitioned FIR signalsinto a plurality of Fourier transformed filter partitions; andconvolution means for convoluting the plurality of Fourier transformedsignal partitions and the plurality of Fourier transformed filterpartitions to provide a plurality of convoluted partitioned outputsignals.
 17. The signal processing system of claim 16, and furthercomprising combiner means for combining the plurality of convolutedpartitioned output signals to obtain an output signal corresponding to atotal spectrum output signal.
 18. The signal processing system of claim17, and further comprising an inverse Fourier transform means forexecuting an inverse Fourier transform operation on the total spectrumoutput signal to obtain a digital output signal.
 19. The signalprocessing system of claim 16, where the first time partitioning meansdivides the input signal into blocks in the time domain, and where theconvolution means executes an overlap-save block convolution of thepartitions provided by the first and second Fourier processors.
 20. Thesignal processing system of claim 16, where the plurality of Fouriertransformed signal partitions of the first Fourier transform means andthe plurality of Fourier transformed filter partitions of the secondFourier transform means have the same bandwidth.
 21. The signalprocessing system of claim 20, where the plurality of Fouriertransformed signal partitions of the first Fourier transform means andthe plurality of Fourier transformed filter partitions of the secondFourier transform means have frequency responses in which the midfrequencies are equally distributed with respect to one another in thefrequency domain.
 22. The signal processing system of claim 16, wherethe first time partitioning means partitions a first portion of theinput signal x[n] to obtain T partitions x_(T)[n] and a second portionof the input signal x[n] to obtain S partitions x_(S)[n], where S and Tare both integers; the first Fourier transform means transforms theinput signal partitions x_(T)[n] to obtain T Fourier transformed signalpartitions X_(T)(ω) and transforms the input signal partitions x_(S)[n]to obtain S Fourier transformed signal partitions X_(S)(ω); the secondtime partitioning means partitions a first portion of the FIR filterinto T time domain partitioned FIR signals FIR_(T)[n] and partitions asecond portion of the FIR filter into S time domain partitioned FIRsignals FIR_(S)[n]; and the second Fourier transform means transformsthe T time domain partitioned FIR signals FIR_(T)[n] to obtaincorresponding Fourier transformed filter partitions FIR_(T)(ω) andtransforms the S time domain partitioned FIR signals FIR_(T)[n] toobtain corresponding Fourier transformed filter partitions FIR_(S)(ω).23. The signal processing system of claim 22, where the convolutionmeans convolutes the Fourier transform signal partitions (X_(T)(ω) andX_(S)(ω)) with the corresponding Fourier transformed filter partitions(FIR_(T)(ω) and FIR_(S)(ω)) to provide a plurality of convolutedpartitioned output signals Y₁(ω), . . . , Y_(T+S)(ω).
 24. The signalprocessing system of claim 23, and further comprising combiner means forcombining the plurality of convoluted partitioned output signals Y₁(ω),. . . , Y_(T+S)(ω) to obtain an output signal corresponding to a totalspectrum output signal.
 25. A method for processing a signal comprising:partitioning a digital input signal in the time domain into a pluralityof time domain partitioned input signals; Fourier transforming theplurality of time partitioned input signals into a plurality of Fouriertransformed signal partitions; time partitioning a finite impulseresponse (FIR) filter in the time domain into a plurality of time domainpartitioned FIR signals; Fourier transforming the plurality of timedomain partitioned FIR signals into a plurality of Fourier transformedfilter signal partitions; and convoluting the plurality of Fouriertransformed signal partitions and is a plurality of Fourier transformedfilter partitions with one another to provide a plurality of convolutedpartitioned output signals.
 26. The method of claim 25, and furthercomprising combining the plurality of convoluted partitioned outputsignals to obtain an output signal corresponding to a total spectrumoutput signal.
 27. The method of claim 26, and further comprisingexecuting an inverse Fourier transform operation on the total spectrumoutput signal to obtain a digital output signal.
 28. The method of claim25, where time partitioning of the digital input signal divides thedigital input signal into blocks in the time domain, and whereconvolution of the plurality of Fourier transformed signal partitionswith the plurality of Fourier transform to filter partitions comprisesexecution of an overlap-save block convolution.
 29. The method of claim25, where the plurality of Fourier transformed signal partitions and theplurality of Fourier transformed filter partitions have the samebandwidth.
 30. The method of claim 29, where the plurality of Fouriertransformed signal partitions and the plurality of Fourier transformfilter partitions have frequency responses in which the mid frequenciesare equally distributed with respect to one another in the frequencydomain.
 31. The method of claim 25, where the time partitioning of thedigital input signal includes partitioning a first portion of thedigital input signal x[n] to obtain T partitions x_(T)[n] and a secondportion of the digital input signal x[n] to obtain S partitionsx_(S)[n], where S and T are both integers; the Fourier transforming ofthe plurality of time partitioned input signals includes Fouriertransforming partitions x_(T)[n] to obtain T Fourier transformed signalpartitions X_(T)(ω) and transforming the input signal partitionsx_(S)[n] to obtain S Fourier transformed signal partitions X_(S)(ω); thetime partitioning of the FIR filter includes partitioning a firstportion of the FIR filter into T time domain partitioned FIR signalsFIR_(T)[n] and partitioning a second portion of the FIR filter into Stime domain partitioned FIR signals FIR_(S)[n]; and the Fouriertransforming of the plurality of time partitioned FIR signals includestransforming the T time domain partitioned FIR signals FIR_(T)[n] toobtain corresponding Fourier transformed filter partitions FIR_(T)(ω)and transforming the S time domain partitioned FIR signals FIR_(T)[n] toobtain corresponding Fourier transformed filter partitions FIR_(S)(ω).32. The method of claim 31, where the convoluting comprises convolutingthe Fourier transform signal partitions (X_(T)(ω) and X_(S)(ω)) with thecorresponding Fourier transformed filter partitions (FIR_(T)(ω) andFIR_(S)(ω)) to provide a plurality of convoluted partitioned outputsignals Y₁(ω), . . . , Y_(T+S)(ω).
 33. The method of claim 32, andfurther comprising combining the plurality of convoluted partitionedoutput signals Y₁(ω), . . . , Y_(T+S)(ω) to obtain an output signalcorresponding to a total spectrum output signal.
 34. A storage mediumcomprising software capable of executing a method for processing asignal comprising, where the method comprises: partitioning a digitalinput signal in the time domain into a plurality of time domainpartitioned input signals; Fourier transforming the plurality of timepartitioned input signals into a plurality of Fourier transformed signalpartitions; time partitioning a finite impulse response (FIR) filter inthe time domain into a plurality of time domain partitioned FIR signals;Fourier transforming the plurality of time domain partitioned FIRsignals into a plurality of Fourier transformed filter partitions; andconvoluting the plurality of Fourier transformed signal partitions withthe plurality of Fourier transformed filter partitions to provide aplurality of convoluted partitioned output signals.
 35. The storagemedium of claim 34, where the method further comprises combining theplurality of convoluted partitioned output signals to obtain an outputsignal corresponding to a total spectrum output signal.
 36. The storagemedium of claim 35, wherein the method further comprises executing aninverse Fourier transform operation on the total spectrum output signalto obtain a digital output signal.
 37. The storage medium of claim 34,where the time partitioning of the digital input signal includespartitioning a first portion of the digital input signal x[n] to obtainT partitions x_(T)[n] and a second portion of the digital input signalx[n] to obtain S partitions x_(S)[n], where S and T are both integers;the Fourier transforming of the plurality of time partitioned inputsignals includes Fourier transforming partitions x_(T)[n] to obtain TFourier transformed signal partitions X_(T)(ω) and transforming theinput signal partitions x_(S)[n] to obtain S Fourier transformed signalpartitions X_(S)(ω); the time partitioning of the FIR filter includespartitioning a first portion of the FIR filter into T time domainpartitioned FIR signals FIR_(T)[n] and partitioning a second portion ofthe FIR filter into S time domain partitioned FIR signals FIR_(S)[n];and the Fourier transforming of the plurality of time partitioned FIRsignals includes transforming the T time domain partitioned FIR signalsFIR_(T)[n] to obtain corresponding Fourier transformed filter partitionsFIR_(T)(ω) and transforming the S time domain partitioned FIR signalsFIR_(T)[n] to obtain corresponding Fourier transformed filter partitionsFIR_(S)(ω).
 38. The storage medium of claim 37, where the convolutingcomprises convoluting the Fourier transformed signal partitions(X_(T)(ω) and X_(S)(ω)) with the corresponding Fourier transformedfilter partitions (FIR_(T)(ω) and FIR_(S)(ω)) to provide a plurality ofconvoluted partitioned output signals Y₁(ω), . . . , Y_(T+S)(ω).
 39. Thestorage medium of claim 38, where the method further comprises combiningthe plurality of convoluted partitioned output signals Y₁(ω), . . . ,Y_(T+S)(ω) to obtain an output signal corresponding to a total spectrumoutput signal.
 40. A signal processing system comprising: a timepartitioner adapted to partition a digital input signal in the timedomain into a plurality of time domain partitioned input signals; aFourier transform processor adapted to provide a plurality of Fouriertransformed signal partitions corresponding to the time domainpartitioned input signal provided by the first time partitioner; memorystorage comprising a second plurality of Fourier transformed signalpartitions corresponding to a plurality of time domain partitioned FIRsignals of an FIR filter; and a convolution processor adapted to providea plurality of convoluted partitioned output signals corresponding to aconvolution of the plurality of Fourier transformed signal partitionsand the plurality of Fourier transformed filter partitions.
 41. Thesignal processing system of claim 40, and further comprising a combineradapted to combine the plurality of convoluted partitioned outputsignals to obtain an output signal corresponding to a total spectrumoutput signal.
 42. The signal processing system of claim 41, and furthercomprising an inverse Fourier transform processor adapted to perform aninverse Fourier transform operation on the total spectrum output signalto obtain a digital output signal.
 43. The signal processing system ofclaim 40, where the first time partitioner divides the digital inputsignal into blocks in the time domain, and where the convolutionprocessor executes an overlap-save block convolution of the plurality ofFourier transformed input signals and plurality of Fourier transformedfilter signals.